From f4b86c2996703f8047f23dc0b99646d119752d7d Mon Sep 17 00:00:00 2001 From: jzmaddock Date: Mon, 17 Nov 2014 18:12:25 +0000 Subject: [PATCH] [polygamma] Switch to new better method for handling negative arguments. --- .../special_functions/detail/polygamma.hpp | 23 +++++++++++++-- test/test_polygamma.hpp | 29 ++++++++++++------- 2 files changed, 40 insertions(+), 12 deletions(-) diff --git a/include/boost/math/special_functions/detail/polygamma.hpp b/include/boost/math/special_functions/detail/polygamma.hpp index 7dbc0d9ea..1baf2f585 100644 --- a/include/boost/math/special_functions/detail/polygamma.hpp +++ b/include/boost/math/special_functions/detail/polygamma.hpp @@ -497,6 +497,7 @@ int index = n - 1; +#if 0 if(index >= (int)table.size()) { // @@ -522,8 +523,8 @@ } } - T sum = 0; int power = n & 1 ? 0 : 1; + T sum = 0; // // Compute the sum of the cosine terms: // @@ -532,6 +533,24 @@ sum += table[index][j] * boost::math::cos_pi(x * power, pol); power += 2; } +#else + if(index >= (int)table.size()) + { + for(int i = (int)table.size() - 1; i < index; ++i) + { + int sin_order = i + 2; + table.push_back(std::vector(i + 2, T(0))); + table[i + 1][1] -= sin_order * table[i][0] / (sin_order - 1); + for(int cos_order = 1; cos_order < i + 1; ++cos_order) + { + table[i + 1][cos_order + 1] += ((cos_order - sin_order) * table[i][cos_order]) / (sin_order - 1); + table[i + 1][cos_order - 1] += (-cos_order * table[i][cos_order]) / (sin_order - 1); + } + } + + } + T sum = boost::math::tools::evaluate_polynomial(&table[index][0], boost::math::cos_pi(x, pol), n); +#endif if(sum == 0) return sum; // @@ -542,7 +561,7 @@ if(s == 0) return sum * boost::math::policies::raise_overflow_error(function, 0, pol); power_terms -= log(fabs(s)) * (n + 1); - power_terms += boost::math::lgamma(T(n + 1)); + power_terms += boost::math::lgamma(T(n)); power_terms += log(fabs(sum)); if(power_terms > boost::math::tools::log_max_value()) diff --git a/test/test_polygamma.hpp b/test/test_polygamma.hpp index 79d637c5d..74296093f 100644 --- a/test/test_polygamma.hpp +++ b/test/test_polygamma.hpp @@ -137,17 +137,17 @@ void test_polygamma(T, const char* name) } }; do_test_polygamma(big_data, name, "Mathematica Data - large arguments"); - boost::array, 471> neg_data = + boost::array, 654> neg_data = { { - { 1, SC_(-12.750), SC_(19.663772856722737612034697464751605) }, { 1, SC_(-12.250), SC_(19.660817549236368273654684043826967) }, { 1, SC_(-11.750), SC_(19.657621376522814505537196503582823) }, { 1, SC_(-11.250), SC_(19.654153659190554029589711115880278) }, { 1, SC_(-10.750), SC_(19.650378280099093364749509767503149) }, { 1, SC_(-10.250), SC_(19.646252424622652795021809881312377) }, { 1, SC_(-9.7500), SC_(19.641724953976865133273035997897957) }, { 1, SC_(-9.2500), SC_(19.636734280660725370869519577921538) }, { 1, SC_(-8.7500), SC_(19.631205558842085383108670448917024) }, { 1, SC_(-8.2500), SC_(19.625046917622010980803778160828770) }, { 1, SC_(-7.7500), SC_(19.618144334352289464741323510141514) }, { 1, SC_(-7.2500), SC_(19.610354539293269015698176691590937) }, { 1, SC_(-6.7500), SC_(19.601495010731061577124257953429755) }, { 1, SC_(-6.2500), SC_(19.591329569019785068016844943671793) }, { 1, SC_(-5.7500), SC_(19.579547136931335925546754524074474) }, { 1, SC_(-5.2500), SC_(19.565729569019785068016844943671793) }, { 1, SC_(-4.7500), SC_(19.549301390239464469970194977760674) }, { 1, SC_(-4.2500), SC_(19.529448389881463072551992335962043) }, { 1, SC_(-3.7500), SC_(19.504980060599575273294294700752364) }, { 1, SC_(-3.2500), SC_(19.474085068082155114074483685443011) }, { 1, SC_(-2.7500), SC_(19.433868949488464162183183589641253) }, { 1, SC_(-2.2500), SC_(19.379410511869137362595193744614609) }, { 1, SC_(-1.7500), SC_(19.301637544529786476232770366500757) }, { 1, SC_(-1.2500), SC_(19.181879647671606498397662880417078) }, { 1, SC_(-0.75000), SC_(18.975106932284888517049096897113002) }, { 1, SC_(-0.25000), SC_(18.541879647671606498397662880417078) }, - { 2, SC_(-12.750), SC_(-124.03079461415823384604153251543681) }, { 2, SC_(-12.250), SC_(124.01896466745858356132308878716344) }, { 2, SC_(-11.750), SC_(-124.03175955222881001960976796032603) }, { 2, SC_(-11.250), SC_(124.01787668541028735821044014586602) }, { 2, SC_(-10.750), SC_(-124.03299241970518808612682102178640) }, { 2, SC_(-10.250), SC_(124.01647202148710491650947992638728) }, { 2, SC_(-9.7500), SC_(-124.03460234084420729198290916496876) }, { 2, SC_(-9.2500), SC_(124.01461482266526541911391108670126) }, { 2, SC_(-8.7500), SC_(-124.03676016548723903560636876475972) }, { 2, SC_(-8.2500), SC_(124.01208782525148933477537240192445) }, { 2, SC_(-7.7500), SC_(-124.03974558822776381694747663647984) }, { 2, SC_(-7.2500), SC_(124.00852603656573370687098416695770) }, { 2, SC_(-6.7500), SC_(-124.04404218787195165891317097369578) }, { 2, SC_(-6.2500), SC_(124.00327776890408296268303058132483) }, { 2, SC_(-5.7500), SC_(-124.05054526159038888901020902683808) }, { 2, SC_(-5.2500), SC_(123.99508576890408296268303058132483) }, { 2, SC_(-4.7500), SC_(-124.06106552130930069964553408642549) }, { 2, SC_(-4.2500), SC_(123.98126436732757934536308673076874) }, { 2, SC_(-3.7500), SC_(-124.07972713378925404561433420306057) }, { 2, SC_(-3.2500), SC_(123.95521103942202265902072971875978) }, { 2, SC_(-2.7500), SC_(-124.11765305971517997154026012898649) }, { 2, SC_(-2.2500), SC_(123.89694977406016558118732052440384) }, { 2, SC_(-1.7500), SC_(-124.21382135423058192495874247308867) }, { 2, SC_(-1.2500), SC_(123.72136678366236036856729308956159) }, { 2, SC_(-0.75000), SC_(-124.58699919679617959259722643810325) }, { 2, SC_(-0.25000), SC_(122.69736678366236036856729308956159) }, - { 3, SC_(-12.750), SC_(1558.5445992104061926890981987122713) }, { 3, SC_(-12.250), SC_(1558.5444945580353369268010524200916) }, { 3, SC_(-11.750), SC_(1558.5443721661542924129644962546503) }, { 3, SC_(-11.250), SC_(1558.5442281134520807137938731609983) }, { 3, SC_(-10.750), SC_(1558.5440573914794724810878018559796) }, { 3, SC_(-10.250), SC_(1558.5438535364058987293402837691373) }, { 3, SC_(-9.7500), SC_(1558.5436081111616066561977307462543) }, { 3, SC_(-9.2500), SC_(1558.5433099660190188764440197184975) }, { 3, SC_(-8.7500), SC_(1558.5429441651175968889289739463186) }, { 3, SC_(-8.2500), SC_(1558.5424903992902266328747639288402) }, { 3, SC_(-7.7500), SC_(1558.5419205916065598210405941045860) }, { 3, SC_(-7.2500), SC_(1558.5411952034044973136368045706704) }, { 3, SC_(-6.7500), SC_(1558.5402573917442935596345188772766) }, { 3, SC_(-6.2500), SC_(1558.5390235064410556263866168800637) }, { 3, SC_(-5.7500), SC_(1558.5373671367583214573691686314356) }, { 3, SC_(-5.2500), SC_(1558.5350913464410556263866168800637) }, { 3, SC_(-4.7500), SC_(1558.5318783056006283387768251220856) }, { 3, SC_(-4.2500), SC_(1558.5271934026830535593466489654603) }, { 3, SC_(-3.7500), SC_(1558.5200920240343420150070566273687) }, { 3, SC_(-3.2500), SC_(1558.5088028182791311925167498981598) }, { 3, SC_(-2.7500), SC_(1558.4897512832936012742663158866280) }, { 3, SC_(-2.2500), SC_(1558.4550231887143400437474491033697) }, { 3, SC_(-1.7500), SC_(1558.3848404165495264159916078748802) }, { 3, SC_(-1.2500), SC_(1558.2209125348505997602540791902467) }, { 3, SC_(-0.75000), SC_(1557.7451069721513589857542067919980) }, { 3, SC_(-0.25000), SC_(1555.7633125348505997602540791902467) }, - { 4, SC_(-12.750), SC_(-24481.574976569827769932951761311307) }, { 4, SC_(-12.250), SC_(24481.574556933476371183897773040987) }, { 4, SC_(-11.750), SC_(-24481.575047799396993548993707180364) }, { 4, SC_(-11.250), SC_(24481.574469931163471195977061446181) }, { 4, SC_(-10.750), SC_(-24481.575154956733102461973007401188) }, { 4, SC_(-10.250), SC_(24481.574336748213717601504674106852) }, { 4, SC_(-9.7500), SC_(-24481.575322130804866489839080372249) }, { 4, SC_(-9.2500), SC_(24481.574124623184691317447595452944) }, { 4, SC_(-8.7500), SC_(-24481.575594518925485881539083161966) }, { 4, SC_(-8.2500), SC_(24481.573770215950618995904133489849) }, { 4, SC_(-7.7500), SC_(-24481.576062438244817112573771089615) }, { 4, SC_(-7.2500), SC_(24481.573142242187841144152395619221) }, { 4, SC_(-6.7500), SC_(-24481.576920863980180344267229271453) }, { 4, SC_(-6.2500), SC_(24481.571944064552838833945395514059) }, { 4, SC_(-5.7500), SC_(-24481.578633607675571219683733120840) }, { 4, SC_(-5.2500), SC_(24481.569427482152838833945395514059) }, { 4, SC_(-4.7500), SC_(-24481.582451925002662084791450344735) }, { 4, SC_(-4.2500), SC_(24481.563410001194361068581610436266) }, { 4, SC_(-3.7500), SC_(-24481.592377214742692673229150129760) }, { 4, SC_(-3.2500), SC_(24481.546101215873022370388764255277) }, { 4, SC_(-2.7500), SC_(-24481.624740671532816130019273586550) }, { 4, SC_(-2.2500), SC_(24481.479910902562510187288086353997) }, { 4, SC_(-1.7500), SC_(-24481.777338295887834105691576149093) }, { 4, SC_(-1.2500), SC_(24481.063714184582527461077650952890) }, { 4, SC_(-0.75000), SC_(-24483.239586168797931089091350052823) }, { 4, SC_(-0.25000), SC_(24473.199394184582527461077650952890) }, - { 5, SC_(-12.750), SC_(492231.26705220367447285602722829798) }, { 5, SC_(-12.250), SC_(492231.26703986858726773334478356804) }, { 5, SC_(-11.750), SC_(492231.26702427051007143797156325129) }, { 5, SC_(-11.250), SC_(492231.26700435743914528929551352935) }, { 5, SC_(-10.750), SC_(492231.26697867164364211329952060413) }, { 5, SC_(-10.250), SC_(492231.26694516501703258064111915631) }, { 5, SC_(-9.7500), SC_(492231.26690091626142628638506805946) }, { 5, SC_(-9.2500), SC_(492231.26684168939311732012547103246) }, { 5, SC_(-8.7500), SC_(492231.26676123004572403423122047499) }, { 5, SC_(-8.2500), SC_(492231.26665011791524038956143753889) }, { 5, SC_(-7.7500), SC_(492231.26649384757753475935425594490) }, { 5, SC_(-7.2500), SC_(492231.26626952775598108546947519306) }, { 5, SC_(-6.7500), SC_(492231.26594002452246170664879905339) }, { 5, SC_(-6.2500), SC_(492231.26544319835253121636119925846) }, { 5, SC_(-5.7500), SC_(492231.26467132548883883596990731311) }, { 5, SC_(-5.2500), SC_(492231.26342993243253121636119925846) }, { 5, SC_(-4.7500), SC_(492231.26135104955223808370232711841) }, { 5, SC_(-4.2500), SC_(492231.25769899818636191601473727961) }, { 5, SC_(-3.7500), SC_(492231.25090337614167956955737997628) }, { 5, SC_(-3.2500), SC_(492231.23733572133772815343491824315) }, { 5, SC_(-2.7500), SC_(492231.20775210042151496050388203390) }, { 5, SC_(-2.2500), SC_(492231.13550447009078633328002916426) }, { 5, SC_(-1.7500), SC_(492230.93030187432148227746333192018) }, { 5, SC_(-1.2500), SC_(492230.21062287457971360836795049513) }, { 5, SC_(-0.75000), SC_(492226.75245080886406232489254933809) }, { 5, SC_(-0.25000), SC_(492198.75334287457971360836795049513) }, - { 6, SC_(-12.750), SC_(-1.1791224761262553923199740571475659e7) }, { 6, SC_(-12.250), SC_(1.1791224761212959953338096554813394e7) }, { 6, SC_(-11.750), SC_(-1.1791224761275698941741584362376857e7) }, { 6, SC_(-11.250), SC_(1.1791224761195566737931185183742355e7) }, { 6, SC_(-10.750), SC_(-1.1791224761298983469279962918313528e7) }, { 6, SC_(-10.250), SC_(1.1791224761163997446137740568065356e7) }, { 6, SC_(-9.7500), SC_(-1.1791224761342381822144610498473088e7) }, { 6, SC_(-9.2500), SC_(1.1791224761103426349211734412564015e7) }, { 6, SC_(-8.7500), SC_(-1.1791224761428342570269073362379294e7) }, { 6, SC_(-8.2500), SC_(1.1791224760979163768967238911569317e7) }, { 6, SC_(-7.7500), SC_(-1.1791224761611690548456004706583543e7) }, { 6, SC_(-7.2500), SC_(1.1791224760702370925869563208323974e7) }, { 6, SC_(-6.7500), SC_(-1.1791224762040456784641593897905007e7) }, { 6, SC_(-6.2500), SC_(1.1791224760018512109221395670440442e7) }, { 6, SC_(-5.7500), SC_(-1.1791224763168189258973034501364332e7) }, { 6, SC_(-5.2500), SC_(1.1791224758085776826021395670440442e7) }, { 6, SC_(-4.7500), SC_(-1.1791224766632825018904254258839318e7) }, { 6, SC_(-4.2500), SC_(1.1791224751536137687542195274483895e7) }, { 6, SC_(-3.7500), SC_(-1.1791224779829886169083430020877813e7) }, { 6, SC_(-3.2500), SC_(1.1791224722787982136529824573562902e7) }, { 6, SC_(-2.7500), SC_(-1.1791224848871927321346804506474521e7) }, { 6, SC_(-2.2500), SC_(1.1791224534791825988329541210690757e7) }, { 6, SC_(-1.7500), SC_(-1.1791225454217875175963567504038405e7) }, { 6, SC_(-1.2500), SC_(1.1791222068440904625468941445147639e7) }, { 6, SC_(-0.75000), SC_(-1.1791239778278671029974833461007258e7) }, { 6, SC_(-0.25000), SC_(1.1791071073496904625468941445147639e7) }, - { 7, SC_(-12.750), SC_(3.3035269585550319411369451657990653e8) }, { 7, SC_(-12.250), SC_(3.3035269585550014530679554645726841e8) }, { 7, SC_(-11.750), SC_(3.3035269585549597724076958273392155e8) }, { 7, SC_(-11.250), SC_(3.3035269585549020632656302567379925e8) }, { 7, SC_(-10.750), SC_(3.3035269585548210560734246359421460e8) }, { 7, SC_(-10.250), SC_(3.3035269585547056321166932680182245e8) }, { 7, SC_(-9.7500), SC_(3.3035269585545384621477943726294791e8) }, { 7, SC_(-9.2500), SC_(3.3035269585542919758450034698830934e8) }, { 7, SC_(-8.7500), SC_(3.3035269585539213080586956648886140e8) }, { 7, SC_(-8.2500), SC_(3.3035269585533516103728829633890794e8) }, { 7, SC_(-7.7500), SC_(3.3035269585524545242332002141349801e8) }, { 7, SC_(-7.2500), SC_(3.3035269585510030650375087453009371e8) }, { 7, SC_(-6.7500), SC_(3.3035269585485817969386206988585281e8) }, { 7, SC_(-6.2500), SC_(3.3035269585444002902560781621765444e8) }, { 7, SC_(-5.7500), SC_(3.3035269585368867935011094629708018e8) }, { 7, SC_(-5.2500), SC_(3.3035269585227536550842381621765444e8) }, { 7, SC_(-4.7500), SC_(3.3035269584947086190323815702711063e8) }, { 7, SC_(-4.2500), SC_(3.3035269584354251332378488235637904e8) }, { 7, SC_(-3.7500), SC_(3.3035269583002256126086884537779074e8) }, { 7, SC_(-3.2500), SC_(3.3035269579619261006329391884897976e8) }, { 7, SC_(-2.7500), SC_(3.3035269570114408444331054633801022e8) }, { 7, SC_(-2.2500), SC_(3.3035269539127781220563177006740899e8) }, { 7, SC_(-1.7500), SC_(3.3035269416026348990428605870784761e8) }, { 7, SC_(-1.2500), SC_(3.3035268771818605685450990413016373e8) }, { 7, SC_(-0.75000), SC_(3.3035263686402030648824099487997220e8) }, { 7, SC_(-0.25000), SC_(3.3035184214649965685450990413016373e8) }, - { 8, SC_(-7.7500), SC_(-1.0569114259666913771892699180522388e10) }, { 8, SC_(-7.2500), SC_(1.0569114259666319911021283350705169e10) }, { 8, SC_(-6.7500), SC_(-1.0569114259667313537290849324034796e10) }, { 8, SC_(-6.2500), SC_(1.0569114259665591328976435838084546e10) }, { 8, SC_(-5.7500), SC_(-1.0569114259668699611772332137177045e10) }, { 8, SC_(-5.2500), SC_(1.0569114259662820559674440318084546e10) }, { 8, SC_(-4.7500), SC_(-1.0569114259674567879524502974422220e10) }, { 8, SC_(-4.2500), SC_(1.0569114259649513356345466704581650e10) }, { 8, SC_(-3.7500), SC_(-1.0569114259707322912185335499305285e10) }, { 8, SC_(-3.2500), SC_(1.0569114259560384126678660185038311e10) }, { 8, SC_(-2.7500), SC_(-1.0569114259982263662729459870590150e10) }, { 8, SC_(-2.2500), SC_(1.0569114258563670778105953357268290e10) }, { 8, SC_(-1.7500), SC_(-1.0569114264464825392297531107332441e10) }, { 8, SC_(-1.2500), SC_(1.0569114231281566759079742278380307e10) }, { 8, SC_(-0.75000), SC_(-1.0569114526390508516485165684831300e10) }, { 8, SC_(-0.25000), SC_(1.0569108819622773799079742278380307e10) }, - { 9, SC_(-7.7500), SC_(3.8051374324233954962308727459400485e11) }, { 9, SC_(-7.2500), SC_(3.8051374324233938918730928010849146e11) }, { 9, SC_(-6.7500), SC_(3.8051374324233908537939910023379690e11) }, { 9, SC_(-6.2500), SC_(3.8051374324233848474063291767903138e11) }, { 9, SC_(-5.7500), SC_(3.8051374324233723728009045648294056e11) }, { 9, SC_(-5.2500), SC_(3.8051374324233449483283804413023138e11) }, { 9, SC_(-4.7500), SC_(3.8051374324232805216534792821594812e11) }, { 9, SC_(-4.2500), SC_(3.8051374324231168248427408936422641e11) }, { 9, SC_(-3.7500), SC_(3.8051374324226598999820108764248547e11) }, { 9, SC_(-3.2500), SC_(3.8051374324212293823321496967578170e11) }, { 9, SC_(-2.7500), SC_(3.8051374324160613219689518915140179e11) }, { 9, SC_(-2.2500), SC_(3.8051374323936280896024439692195702e11) }, { 9, SC_(-1.7500), SC_(3.8051374322693593017285422874024520e11) }, { 9, SC_(-1.2500), SC_(3.8051374313023439288413955260640509e11) }, { 9, SC_(-0.75000), SC_(3.8051374187988955981988925091310821e11) }, { 9, SC_(-0.25000), SC_(3.8051370416629108357213955260640509e11) }, + { SC_(1.0), SC_(-12.750), SC_(19.663772856722737612034697464751605) }, { SC_(1.0), SC_(-12.250), SC_(19.660817549236368273654684043826967) }, { SC_(1.0), SC_(-11.750), SC_(19.657621376522814505537196503582823) }, { SC_(1.0), SC_(-11.250), SC_(19.654153659190554029589711115880278) }, { SC_(1.0), SC_(-10.750), 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SC_(-1.0569114526390508516485165684831300e10) }, { SC_(8.0), SC_(-0.25000), SC_(1.0569108819622773799079742278380307e10) }, + { SC_(9.0), SC_(-7.7500), SC_(3.8051374324233954962308727459400485e11) }, { SC_(9.0), SC_(-7.2500), SC_(3.8051374324233938918730928010849146e11) }, { SC_(9.0), SC_(-6.7500), SC_(3.8051374324233908537939910023379690e11) }, { SC_(9.0), SC_(-6.2500), SC_(3.8051374324233848474063291767903138e11) }, { SC_(9.0), SC_(-5.7500), SC_(3.8051374324233723728009045648294056e11) }, { SC_(9.0), SC_(-5.2500), SC_(3.8051374324233449483283804413023138e11) }, { SC_(9.0), SC_(-4.7500), SC_(3.8051374324232805216534792821594812e11) }, { SC_(9.0), SC_(-4.2500), SC_(3.8051374324231168248427408936422641e11) }, { SC_(9.0), SC_(-3.7500), SC_(3.8051374324226598999820108764248547e11) }, { SC_(9.0), SC_(-3.2500), SC_(3.8051374324212293823321496967578170e11) }, { SC_(9.0), SC_(-2.7500), SC_(3.8051374324160613219689518915140179e11) }, { SC_(9.0), SC_(-2.2500), SC_(3.8051374323936280896024439692195702e11) }, { SC_(9.0), SC_(-1.7500), SC_(3.8051374322693593017285422874024520e11) }, { SC_(9.0), SC_(-1.2500), SC_(3.8051374313023439288413955260640509e11) }, { SC_(9.0), SC_(-0.75000), SC_(3.8051374187988955981988925091310821e11) }, { SC_(9.0), SC_(-0.25000), SC_(3.8051370416629108357213955260640509e11) }, { SC_(10.0), SC_(-7.7500), SC_(-1.5220204740668341333676731352020598e13)}, { SC_(10.0), SC_(-7.2500), SC_(1.5220204740668340669650877835677384e13) }, { SC_(10.0), SC_(-6.7500), SC_(-1.5220204740668341932700845125388608e13) }, { SC_(10.0), SC_(-6.2500), SC_(1.5220204740668339422138220784050543e13) }, { SC_(10.0), SC_(-5.7500), SC_(-1.5220204740668344670625746819834321e13) }, { SC_(10.0), SC_(-5.2500), SC_(1.5220204740668333038285748986372463e13) }, { SC_(10.0), SC_(-4.7500), SC_(-1.5220204740668360644738342521168221e13) }, { SC_(10.0), SC_(-4.2500), SC_(1.5220204740668289586193246215389596e13) }, { SC_(10.0), SC_(-3.7500), SC_(-1.5220204740668491301932335869743932e13) }, { SC_(10.0), SC_(-3.2500), SC_(1.5220204740667845482073107110240315e13) }, { SC_(10.0), SC_(-2.7500), SC_(-1.5220204740670250922735818265720155e13) }, { SC_(10.0), SC_(-2.2500), SC_(1.5220204740659352776617813040228546e13) }, { SC_(10.0), SC_(-1.7500), SC_(-1.5220204740723597111914149030851634e13) }, { SC_(10.0), SC_(-1.2500), SC_(1.5220204740174337594057347065492760e13) }, { SC_(10.0), SC_(-0.75000), SC_(-1.5220204748421004942502520332720988e13) }, { SC_(10.0), SC_(-0.25000), SC_(1.5220204428462791119561347065492760e13) }, { SC_(11.0), SC_(-7.7500), SC_(6.6969403856797204470999075620782555e14)}, { SC_(11.0), SC_(-7.2500), SC_(6.6969403856797204443997065278152669e14) }, { SC_(11.0), SC_(-6.7500), SC_(6.6969403856797204385976298181981934e14) }, { SC_(11.0), SC_(-6.2500), SC_(6.6969403856797204254719282828940321e14) }, { SC_(11.0), SC_(-5.7500), SC_(6.6969403856797203939795943831775966e14) }, { SC_(11.0), SC_(-5.2500), SC_(6.6969403856797203131161247792548979e14) }, { SC_(11.0), SC_(-4.7500), SC_(6.6969403856797200883878751610651220e14) }, { SC_(11.0), SC_(-4.2500), SC_(6.6969403856797194026913294831009712e14) }, { SC_(11.0), SC_(-3.7500), SC_(6.6969403856797170626423300519402108e14) }, { SC_(11.0), SC_(-3.2500), SC_(6.6969403856797079082317494121441662e14) }, { SC_(11.0), SC_(-2.7500), SC_(6.6969403856796654470987612349915749e14) }, { SC_(11.0), SC_(-2.2500), SC_(6.6969403856794204628163394590053064e14) }, { SC_(11.0), SC_(-1.7500), SC_(6.6969403856775315995316280043863158e14) }, { SC_(11.0), SC_(-1.2500), SC_(6.6969403856557086094467166780182235e14) }, { SC_(11.0), SC_(-0.75000), SC_(6.6969403851936945358946446654116707e14) }, { SC_(11.0), SC_(-0.25000), SC_(6.6969403582250925196910686780182235e14) }, { SC_(12.0), SC_(-7.7500), SC_(-3.2145233093874118337222380549030432e16)}, { SC_(12.0), SC_(-7.2500), SC_(3.2145233093874118336089459241510371e16) }, { SC_(12.0), SC_(-6.7500), SC_(-3.2145233093874118338538862264211861e16) }, { SC_(12.0), SC_(-6.2500), SC_(3.2145233093874118332956585600971684e16) }, { SC_(12.0), SC_(-5.7500), SC_(-3.2145233093874118346470957452659967e16) }, { SC_(12.0), SC_(-5.2500), SC_(3.2145233093874118311384271328272970e16) }, { SC_(12.0), SC_(-4.7500), SC_(-3.2145233093874118410246620594666049e16) }, { SC_(12.0), SC_(-4.2500), SC_(3.2145233093874118103287175260580644e16) }, { SC_(12.0), SC_(-3.7500), SC_(-3.2145233093874119174645495148550237e16) }, { SC_(12.0), SC_(-3.2500), SC_(3.2145233093874114857792705593486958e16) }, { SC_(12.0), SC_(-2.7500), SC_(-3.2145233093874135691619437169973801e16) }, { SC_(12.0), SC_(-2.2500), SC_(3.2145233093874008724100861918481841e16) }, { SC_(12.0), SC_(-1.7500), SC_(-3.2145233093875066825103277125147005e16) }, { SC_(12.0), SC_(-1.2500), SC_(3.2145233093861362402303729768622063e16) }, { SC_(12.0), SC_(-0.75000), SC_(-3.2145233094206840811597208557586761e16) }, { SC_(12.0), SC_(-0.25000), SC_(3.2145233067527970956138307688622063e16) }, @@ -160,6 +160,15 @@ void test_polygamma(T, const char* name) { SC_(2.0), SC_(-9.5), SC_(-0.0099751442477151692853059194570941025) }, { SC_(4.0), SC_(-9.5), SC_(-0.00059506011900940675655749713967447346) }, { SC_(6.0), SC_(-9.5), SC_(-0.00011794286977626608581527674104044053) }, { SC_(8.0), SC_(-9.5), SC_(-0.000048934615584055214532361558113243801) }, { SC_(10.0), SC_(-9.5), SC_(-0.000034696555222805555969152083201249795) }, { SC_(12.0), SC_(-9.5), SC_(-0.000037470635416758472254487967117333555) }, { SC_(14.0), SC_(-9.5), SC_(-0.000057218576281198884425118075685027774) }, { SC_(16.0), SC_(-9.5), SC_(-0.00011728023376485851827598955099805232) }, { SC_(18.0), SC_(-9.5), SC_(-0.00031049110045758006635527458576736345) }, { SC_(20.0), SC_(-9.5), SC_(-0.0010307637762451416598018081796345932) }, { SC_(2.0), SC_(-9.5367431640625000000000000000000000e-7), SC_(2.3058430092136939495958800005662742e18) }, { SC_(2.0), SC_(-4.7683715820312500000000000000000000e-7), SC_(1.8446744073709551613595883097126372e19) }, { SC_(2.0), SC_(-2.3841857910156250000000000000000000e-7), SC_(1.4757395258967641292559588464540430e20) }, { SC_(2.0), SC_(-1.1920928955078125000000000000000000e-7), SC_(1.1805916207174113034215958854195427e21) }, { SC_(2.0), SC_(-5.9604644775390625000000000000000000e-8), SC_(9.4447329657392904273895958858066118e21) }, { SC_(2.0), SC_(-2.9802322387695312500000000000000000e-8), SC_(7.5557863725914323419133595886000146e22) }, { SC_(2.0), SC_(-1.4901161193847656250000000000000000e-8), SC_(6.0446290980731458735308559588609691e23) }, { SC_(2.0), SC_(-7.4505805969238281250000000000000000e-9), SC_(4.8357032784585166988247015958861453e24) }, { SC_(2.0), SC_(-3.7252902984619140625000000000000000e-9), SC_(3.8685626227668133590597629595886169e25) }, { SC_(2.0), SC_(-1.8626451492309570312500000000000000e-9), SC_(3.0948500982134506872478105359588618e26) }, { SC_(2.0), SC_(-9.3132257461547851562500000000000000e-10), SC_(2.4758800785707605497982484455958862e27) }, { SC_(2.0), SC_(-4.6566128730773925781250000000000000e-10), SC_(1.9807040628566084398385987581595886e28) }, { SC_(2.0), SC_(-2.3283064365386962890625000000000000e-10), SC_(1.5845632502852867518708790066959589e29) }, { SC_(2.0), SC_(-1.1641532182693481445312500000000000e-10), SC_(1.2676506002282294014967032053735959e30) }, { SC_(2.0), SC_(-5.8207660913467407226562500000000000e-11), SC_(1.0141204801825835211973625643005596e31) }, { SC_(2.0), SC_(-2.9103830456733703613281250000000000e-11), SC_(8.1129638414606681695789005144061596e31) }, { SC_(2.0), SC_(-1.4551915228366851806640625000000000e-11), SC_(6.4903710731685345356631204115250960e32) }, { SC_(2.0), SC_(-7.2759576141834259033203125000000000e-12), SC_(5.1922968585348276285304963292200936e33) }, { SC_(2.0), SC_(-3.6379788070917129516601562500000000e-12), SC_(4.1538374868278621028243970633760766e34) }, { SC_(2.0), SC_(-1.8189894035458564758300781250000000e-12), SC_(3.3230699894622896822595176507008614e35) }, { SC_(2.0), SC_(-9.0949470177292823791503906250000000e-13), SC_(2.6584559915698317458076141205606891e36) }, { SC_(2.0), SC_(-4.5474735088646411895751953125000000e-13), SC_(2.1267647932558653966460912964485513e37) }, { SC_(2.0), SC_(-2.2737367544323205947875976562500000e-13), SC_(1.7014118346046923173168730371588411e38) }, { SC_(2.0), SC_(-1.1368683772161602973937988281250000e-13), SC_(1.3611294676837538538534984297270728e39) }, { SC_(2.0), SC_(-5.6843418860808014869689941406250000e-14), SC_(1.0889035741470030830827987437816583e40) }, { SC_(2.0), SC_(-2.8421709430404007434844970703125000e-14), SC_(8.7112285931760246646623899502532662e40) }, { SC_(2.0), SC_(-1.4210854715202003717422485351562500e-14), SC_(6.9689828745408197317299119602026130e41) }, { SC_(2.0), SC_(-7.1054273576010018587112426757812500e-15), SC_(5.5751862996326557853839295681620904e42) }, { SC_(2.0), SC_(-3.5527136788005009293556213378906250e-15), SC_(4.4601490397061246283071436545296723e43) }, { SC_(2.0), SC_(-1.7763568394002504646778106689453125e-15), SC_(3.5681192317648997026457149236237378e44) }, { SC_(2.0), SC_(-8.8817841970012523233890533447265625e-16), SC_(2.8544953854119197621165719388989903e45) }, { SC_(2.0), SC_(-4.4408920985006261616945266723632812e-16), SC_(2.2835963083295358096932575511191922e46) }, { SC_(2.0), SC_(-2.2204460492503130808472633361816406e-16), SC_(1.8268770466636286477546060408953538e47) }, { SC_(2.0), SC_(-1.1102230246251565404236316680908203e-16), SC_(1.4615016373309029182036848327162830e48) }, { SC_(2.0), SC_(-5.5511151231257827021181583404541016e-17), SC_(1.1692013098647223345629478661730264e49) }, { SC_(2.0), SC_(-2.7755575615628913510590791702270508e-17), SC_(9.3536104789177786765035829293842113e49) }, { SC_(2.0), SC_(-1.3877787807814456755295395851135254e-17), SC_(7.4828883831342229412028663435073691e50) }, { SC_(2.0), SC_(-6.9388939039072283776476979255676270e-18), SC_(5.9863107065073783529622930748058952e51) }, { SC_(2.0), SC_(-3.4694469519536141888238489627838135e-18), SC_(4.7890485652059026823698344598447162e52) }, { SC_(2.0), SC_(-1.7347234759768070944119244813919067e-18), SC_(3.8312388521647221458958675678757730e53) }, { SC_(2.0), SC_(-8.6736173798840354720596224069595337e-19), SC_(3.0649910817317777167166940543006184e54) }, { SC_(2.0), SC_(-4.3368086899420177360298112034797668e-19), SC_(2.4519928653854221733733552434404947e55) }, { SC_(2.0), SC_(-2.1684043449710088680149056017398834e-19), SC_(1.9615942923083377386986841947523958e56) }, { SC_(2.0), SC_(-1.0842021724855044340074528008699417e-19), SC_(1.5692754338466701909589473558019166e57) }, { SC_(2.0), SC_(-5.4210108624275221700372640043497086e-20), SC_(1.2554203470773361527671578846415333e58) }, { SC_(2.0), SC_(-2.7105054312137610850186320021748543e-20), SC_(1.0043362776618689222137263077132266e59) }, { SC_(2.0), SC_(-1.3552527156068805425093160010874271e-20), SC_(8.0346902212949513777098104617058130e59) }, { SC_(2.0), SC_(-6.7762635780344027125465800054371357e-21), SC_(6.4277521770359611021678483693646504e60) }, { SC_(2.0), SC_(-3.3881317890172013562732900027185678e-21), SC_(5.1422017416287688817342786954917203e61) }, { SC_(3.0), SC_(-9.5367431640625000000000000000000000e-7), SC_(7.2535549176877750482370624939631357e24) }, { SC_(3.0), SC_(-4.7683715820312500000000000000000000e-7), SC_(1.1605687868300440077179290249395127e26) }, { SC_(3.0), SC_(-2.3841857910156250000000000000000000e-7), SC_(1.8569100589280704123486863424939453e27) }, { SC_(3.0), SC_(-1.1920928955078125000000000000000000e-7), SC_(2.9710560942849126597578981382493942e28) }, { SC_(3.0), SC_(-5.9604644775390625000000000000000000e-8), SC_(4.7536897508558602556126370202249394e29) }, { SC_(3.0), SC_(-2.9802322387695312500000000000000000e-8), SC_(7.6059036013693764089802192322624939e30) }, { SC_(3.0), SC_(-1.4901161193847656250000000000000000e-8), SC_(1.2169445762191002254368350771610249e32) }, { SC_(3.0), SC_(-7.4505805969238281250000000000000000e-9), SC_(1.9471113219505603606989361234575425e33) }, { SC_(3.0), SC_(-3.7252902984619140625000000000000000e-9), SC_(3.1153781151208965771182977975320582e34) }, { SC_(3.0), SC_(-1.8626451492309570312500000000000000e-9), SC_(4.9846049841934345233892764760512922e35) }, { SC_(3.0), SC_(-9.3132257461547851562500000000000000e-10), SC_(7.9753679747094952374228423616820675e36) }, { SC_(3.0), SC_(-4.6566128730773925781250000000000000e-10), SC_(1.2760588759535192379876547778691308e38) }, { SC_(3.0), SC_(-2.3283064365386962890625000000000000e-10), SC_(2.0416942015256307807802476445906093e39) }, { SC_(3.0), SC_(-1.1641532182693481445312500000000000e-10), SC_(3.2667107224410092492483962313449748e40) }, { SC_(3.0), SC_(-5.8207660913467407226562500000000000e-11), SC_(5.2267371559056147987974339701519597e41) }, { SC_(3.0), 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SC_(-1237.1507698016190706446362670415721) }, { SC_(9.0), SC_(-0.50000023841857910156250000000000000), SC_(7.4318457240443082449903207673842183e8) }, { SC_(10.), SC_(-0.50000023841857910156250000000000000), SC_(-120071.43228224150936593763797588950) }, { SC_(11.), SC_(-0.50000023841857910156250000000000000), SC_(3.2699873394114574294629126382636465e11) }, { SC_(12.), SC_(-0.50000023841857910156250000000000000), SC_(-5.1113082699448800419004327980237078e7) }, { SC_(13.), SC_(-0.50000023841857910156250000000000000), SC_(2.0404703892677090523475108203530504e14) }, { SC_(14.), SC_(-0.50000023841857910156250000000000000), SC_(-4.1064004123360078851054877806228941e10) }, { SC_(15.), SC_(-0.50000023841857910156250000000000000), SC_(1.7139949675921973682361201187974158e17) }, { SC_(16.), SC_(-0.50000023841857910156250000000000000), SC_(-4.4482167955078907488604509935932075e13) }, { SC_(17.), SC_(-0.50000023841857910156250000000000000), SC_(1.8648265054954360818722434334340996e20) }, { SC_(18.), SC_(-0.50000023841857910156250000000000000), SC_(-6.0825438456286690418846111378451293e16) }, { SC_(19.), SC_(-0.50000023841857910156250000000000000), SC_(2.5510826566134749972709942636451521e23) }, { SC_(20.), SC_(-0.50000023841857910156250000000000000), SC_(-1.0218237211995580504353583819436291e20) }, { SC_(21.), SC_(-0.50000023841857910156250000000000000), SC_(4.2858188626062237162861505116019247e26) }, + { SC_(1.0), SC_(-0.49999976158142089843750000000000000), SC_(8.9348020029496580439061915046847633) }, { SC_(2.0), SC_(-0.49999976158142089843750000000000000), SC_(-0.82875053191374905338324754695139008) }, { SC_(3.0), SC_(-0.49999976158142089843750000000000000), SC_(193.40909020611360344139301017638823) }, { SC_(4.0), SC_(-0.49999976158142089843750000000000000), SC_(-3.4705850676169879410688441586536334) }, { SC_(5.0), SC_(-0.49999976158142089843750000000000000), SC_(15371.113538314606395712740903053532) }, { SC_(6.0), SC_(-0.49999976158142089843750000000000000), SC_(-42.842641692316412901148012739850716) }, { SC_(7.0), SC_(-0.49999976158142089843750000000000000), SC_(2.5806802179540060642078552424908302e6) }, { SC_(8.0), SC_(-0.49999976158142089843750000000000000), SC_(-882.77275028362734588789574976519641) }, { SC_(9.0), SC_(-0.49999976158142089843750000000000000), SC_(7.4318457238435175594844592942103986e8) }, { SC_(10.), SC_(-0.49999976158142089843750000000000000), SC_(35853.714744150436439369297880163123) }, { SC_(11.), SC_(-0.49999976158142089843750000000000000), SC_(3.2699873393997058844655604408250598e11) }, { SC_(12.), SC_(-0.49999976158142089843750000000000000), SC_(4.6184127480583821271680125577145403e7) }, { SC_(13.), SC_(-0.49999976158142089843750000000000000), SC_(2.0404703892667592897735663251491103e14) }, { SC_(14.), SC_(-0.49999976158142089843750000000000000), SC_(4.0665644827064704770358560360332387e10) }, { SC_(15.), SC_(-0.49999976158142089843750000000000000), SC_(1.7139949675920960909557128308150980e17) }, { SC_(16.), SC_(-0.49999976158142089843750000000000000), SC_(4.4439689184846657075559083382657063e13) }, { SC_(17.), SC_(-0.49999976158142089843750000000000000), SC_(1.8648265054954223096603082369745267e20) }, { SC_(18.), SC_(-0.49999976158142089843750000000000000), SC_(6.0819661971925807709274166342293111e16) }, { SC_(19.), SC_(-0.49999976158142089843750000000000000), SC_(2.5510826566134726713883235580466596e23) }, { SC_(20.), SC_(-0.49999976158142089843750000000000000), SC_(1.0218139657405687413065653078640133e20) }, { SC_(21.), SC_(-0.49999976158142089843750000000000000), SC_(4.2858188626062232387116210610555278e26) }, } }; do_test_polygamma(neg_data, name, "Mathematica Data - negative arguments");